Secondary reflectors for solar collectors and methods of making the same
The present disclosure relates to a device that includes a reflecting surface having a length aligned along a first axis (z), where a cross-section of the reflecting surface in a plane perpendicular to the first axis (z) forms a curve comprising a concave section positioned between a first endpoint and a second endpoint, at least a portion of the concave section is accurately approximated by a polynomial equation, an aperture is formed by a straight line connecting the first endpoint to the second endpoint, and the concave section is configured to focus a plurality of beams of light passing through the aperture onto a focal point.
1. A device comprising:
a reflecting surface for a concentrating solar system using a tracking system, the reflector surface having a length aligned along a first axis (z), wherein:
a cross-section of the reflecting surface in a plane perpendicular to the first axis (z) forms a curve comprising a concave section positioned between a first endpoint and a second endpoint,
at least a portion of the concave section is accurately approximated by a polynomial equation,
the concave section is configured to focus a plurality of beams of light onto a focal point,
the plane contains a second axis (x) that is perpendicular to the first axis (z) and a third axis (y) that is perpendicular to the second axis (x),
the third axis (y) intersects the second axis (x) to form a dimensionless xy-coordinate system having an origin of (0, 0) at the intersection,
the concave section is positioned in the dimensionless xy-coordinate system,
the concave section comprises a first portion that starts at the first endpoint positioned at (1, 0) and terminates at an intermediate point at (0, D),
D is a dimensionless number between 0.55 and 0.93, inclusively,
the polynomial equation is a third-order polynomial equation defined as
y=a′x 3 +b′x 2 +c′x+D
a′ is between −0.15 and −0.09, inclusively,
b′ is between −0.45 and −0.07, inclusively,
c′ is between 0.10 and 0.24, inclusively, and
a′, b′, and c′ are all dimensionless numbers.
2. The device of claim 1 , further comprising an aperture formed by a straight line connecting the first endpoint to the second endpoint, wherein the focal point is positioned at least partially within an area enclosed by the concave section and the straight line.
3. The device of claim 1 , further comprising an aperture formed by a straight line connecting the first endpoint to the second endpoint, wherein the focal point is positioned outside an area enclosed by the concave section and the straight line.
4. The device of claim 1 , wherein the first portion has a slope of 1.0 at the intermediate point.
5. The device of claim 1 , wherein the first portion has a slope not equal to 1.0 at the intermediate point.
6. The device of claim 1 , wherein the first portion is accurately described within the xy-coordinate system by the polynomial equation.
7. The device of claim 1 , wherein
b′ is between −0.40 and −0.07, inclusively.
8. The device of claim 7 , wherein c′ is between 0.15 and 0.24, inclusively.
9. The device of claim 8 , wherein D is between 0.60 and 0.93, inclusively.
10. The device of claim 1 , wherein the first portion is accurately described as indicated by a regression R 2 value between 0.999 and 1.0 inclusively.
11. The device of claim 1 , further comprising an absorber tube having a circular cross-section positioned at the focal point.
12. The device of claim 11 , wherein the absorber tube is configured so that a heat-transfer fluid can flow through the absorber tube.
13. The device of claim 1 , wherein:
the concave section further comprises a second portion that starts at the second endpoint positioned at (−1, 0) and terminates at the intermediate point, and
the second portion is a symmetrical, mirror-image of the first portion.